Friction Factor Calculator with Steps - Darcy-Weisbach Head Loss

Fluid Density (ρ) kg/m³

Dynamic Viscosity (μ) Pa·s

Velocity (v) m/s

Pipe Diameter (D) m

Pipe Length (L) m

Pipe Roughness (ε) mm (commercial steel ≈ 0.045)

Head Loss (hf):

What is Friction Factor and Head Loss?

As fluid flows through a pipe, friction against the pipe wall causes a pressure (or head) loss along its length. The Darcy-Weisbach equation calculates this:

hf = f × (L/D) × (v² / 2g)

where f is the dimensionless Darcy friction factor, which depends on the flow regime and pipe roughness.

How f is Found

Regime	Formula for f
Laminar (Re < 2300)	f = 64 / Re
Turbulent (Re > 4000)	Swamee-Jain approximation of Colebrook-White

This calculator uses the Swamee-Jain equation for turbulent flow, an explicit approximation of the implicit Colebrook-White equation that's accurate to within about 1% and doesn't require iterative solving.

Why It Matters

Head loss directly determines how much extra pump head (and therefore power) is needed to overcome pipe friction — this is usually the single biggest contributor to total system head in a piping design, ahead of static elevation change in many industrial layouts.

Solved Examples (Practice Problems)

Click "Try This Example" to auto-fill the calculator above and see the full step-by-step working.

Example 1 — Water in a commercial steel pipe (turbulent)

Water (ρ = 998 kg/m³, μ = 0.001 Pa·s) flows at 2 m/s through a 100 mm diameter, 50 m long commercial steel pipe (ε = 0.045 mm). Find the head loss.

Example 2 — Oil in a small pipe (laminar)

An oil (ρ = 900 kg/m³, μ = 0.05 Pa·s) flows at 0.3 m/s through a 20 mm diameter, 10 m long pipe. Find the head loss (roughness doesn't affect laminar flow, but the field still needs a value).

Example 3 — Using a Reynolds number you already calculated

You already found Re = 50,000 elsewhere. Velocity is 1.5 m/s, pipe diameter 150 mm, length 100 m, roughness 0.15 mm (cast iron). Find the head loss.

Worked Solutions in Full

Each example below is solved completely, using exactly the method the calculator uses: Reynolds number first, then the friction factor, then the Darcy-Weisbach equation.

Example 1 — Water in commercial steel pipe (turbulent)

Given: ρ = 998 kg/m³, μ = 0.001 Pa·s, v = 2 m/s, D = 0.1 m, L = 50 m, ε = 0.045 mm

Step 1 — Reynolds number: Re = 998 × 2 × 0.1 / 0.001 = 199,600. This is above 4,000, so the flow is turbulent.

Step 2 — Relative roughness: ε / D = 0.000045 / 0.1 = 0.00045

Step 3 — Swamee-Jain terms: ε/(3.7D) = 0.0001216 and 5.74 / Re^0.9 = 0.0000974, which add to 0.0002191

Step 4 — Friction factor: log₁₀(0.0002191) = -3.6594, so f = 0.25 / (-3.6594)² = 0.01867

Step 5 — Velocity head: v² / 2g = 4 / 19.62 = 0.2039 m

Step 6 — Head loss: h_f = f × (L/D) × v²/2g = 0.01867 × (50/0.1) × 0.2039 = 1.903 m

Step 7 — Convert to pressure drop: ΔP = ρ g h_f = 998 × 9.81 × 1.903 = 18,631 Pa ≈ 18.6 kPa

Answer: f ≈ 0.01867, head loss ≈ 1.90 m of water over 50 m of pipe.

Example 2 — Oil in a small pipe (laminar)

Given: ρ = 900 kg/m³, μ = 0.05 Pa·s, v = 0.3 m/s, D = 0.02 m, L = 10 m

Step 1 — Reynolds number: Re = 900 × 0.3 × 0.02 / 0.05 = 108. This is below 2,300, so the flow is laminar.

Step 2 — Friction factor: For laminar flow f = 64 / Re = 64 / 108 = 0.5926. Roughness plays no part here.

Step 3 — Velocity head: v² / 2g = 0.09 / 19.62 = 0.00459 m

Step 4 — Head loss: h_f = 0.5926 × (10/0.02) × 0.00459 = 1.359 m

Answer: f ≈ 0.5926, head loss ≈ 1.36 m of oil.

Example 3 — Reynolds number already known (cast iron)

Given: Re = 50,000, v = 1.5 m/s, D = 0.15 m, L = 100 m, ε = 0.15 mm

Step 1 — Flow regime: Re = 50,000 is well above 4,000, so use the turbulent equation.

Step 2 — Relative roughness: ε / D = 0.00015 / 0.15 = 0.0010

Step 3 — Swamee-Jain terms: ε/(3.7D) = 0.0002703 and 5.74 / Re^0.9 = 0.0003387, which add to 0.0006090

Step 4 — Friction factor: log₁₀(0.0006090) = -3.2154, so f = 0.25 / (-3.2154)² = 0.02418

Step 5 — Head loss: v² / 2g = 0.1147 m, so h_f = 0.02418 × (100/0.15) × 0.1147 = 1.849 m

Answer: f ≈ 0.02418, head loss ≈ 1.85 m.

Practical Notes and Common Mistakes

Friction loss is normally the largest part of the head a pump has to develop in an industrial piping system. Adding it to the static head (and any pressure difference) gives the total head that feeds the Pump Power Calculator, and the suction-side portion feeds the NPSH Calculator.

Mistakes that give wrong answers

Darcy versus Fanning. This page uses the Darcy friction factor. A Fanning factor is one quarter of it, so putting a Fanning value into the Darcy-Weisbach equation understates head loss by a factor of four.
Roughness in the wrong unit. Roughness is quoted in millimetres but must be divided by the diameter in metres. The calculator handles the conversion; hand calculations often miss it.
Forgetting fittings. The result is for straight pipe only. Valves, bends, entrances and exits add minor losses that must be added separately.
Using a turbulent formula for laminar flow. Always check Re first, as the calculator does.
Trusting values near Re 2,300–5,000. The Swamee-Jain equation is specified for Re from about 5,000 upward, and flow in the transitional zone is uncertain in real life. Treat results in that band as rough estimates.

Typical absolute roughness values

Pipe material	Roughness ε (mm)
Drawn tubing, glass, PVC	0.0015
Commercial steel, wrought iron	0.045
Galvanised iron	0.15
Cast iron	0.26
Concrete	0.3 – 3

Frequently Asked Questions

What roughness value should I use for my pipe material?

Common values: commercial steel ≈ 0.045 mm, drawn tubing/copper ≈ 0.0015 mm, cast iron ≈ 0.15-0.26 mm, PVC/plastic ≈ 0.0015 mm, concrete ≈ 0.3-3 mm depending on finish. When in doubt, commercial steel's value is a reasonable default for typical industrial piping.

Does roughness matter for laminar flow?

No — in laminar flow, friction factor depends only on Reynolds number (f = 64/Re), not on pipe roughness. Roughness only starts to matter once flow becomes turbulent, where it affects how the flow interacts with the pipe wall.

How accurate is the Swamee-Jain approximation vs the real Colebrook-White equation?

Swamee-Jain is accurate to within about 1% of the full iterative Colebrook-White solution across its valid range (Re between 5,000 and 100 million, relative roughness between 0.000001 and 0.01) — accurate enough for essentially all practical engineering design work.

Is head loss the same as pressure drop?

They're directly related but not the same units — head loss (hf) is in meters, pressure drop (ΔP) is in Pascals. Convert with ΔP = ρ × g × hf.

Related Tool

Need the Reynolds number first? Use the Reynolds Number Calculator — this tool picks up exactly where that one leaves off.